We all know of Memory Alpha in the show along with the website. But for the sake of redundancy across the Milkyway Galaxy, how many Central Libraries should there be IYO?
Probably as many as there are member planets (at least) in any given time frame. If we think about it, each planet that joined UFP would also have to have its own SF Academy. I mean, it doesn't make sense to ship people across over 8000 Ly's to Earth for example at slow warp... and I'd posit that about 1% to 5% of all UFP citizens would actually be in SF (given how prominent the organisation is)... if not 10% in the 24th century (that would be around 10 billion to 100 billion people in total). Usually only developed planets/species join up the UFP, and it would make sense SF would create its own shipbuilding facilities/complexes in each... initially sending a detachment of SF officers to help with the transition and train the local population in using the technology in question (or the other way around if the member species/planet is more advanced and the technology would nee to be integrated into Starfleet's). Each member solar system would have its own version of 'Utopia Planitia' and similarly developed planetary defenses (planetary shields, automated platforms with phasers and torpedoes and loads of scanners spread throughout the solar system) - or those systems would be brough 'up to par' with what Earth has in the first year of the planet/system joining. Anyway, back to the premise at hand... in terms of central libraries... Memory Alpha would likely retain the status of a 'central library' (as in singular)... all others would probably be backups (but with exactly the same function) spread across UFP space (some perhaps in remote regions to safeguard data which is constantly updated with exploration ships sending back data) - similar to that seed ship (the USS Tikhov - though instead of just having one ship, wouldn't it make sense there are hundreds with adjacent 'vaults' on member planets)?
I've tended to view Memory Alpha as being more akin to the Library of Congress in the US. Every Federation member world may have its own central library that coordinates and keeps up to date with Memory Alpha (and perhaps vice-versa).
Memory Alpha Could it be a combination of the US Library of Congress + Wikipedia + deeper Academic, Technical, Historic, General Culture, & Artistic Archives?
If you remove the Wikipedia element, the rest really describes the US Library of Congress. It's as much an all-encompassing government-run research facility as it is a data depository. Unlike Wikipedia, not just anyone can edit things on a whim.
Replace Wikipedia with Encyclopedia Britannica and other Established Encyclopedia brands that do proper research & proofing.
I think Memory Alpha is the head library, in the sense it's where the administrative offices are. Other branches are located through out the Federation. All branches are updated constantly via sub-space.